# Ray-wave correspondence in an unstable quasistadium laser resonator

## Abstract

The relation between unstable periodic orbits and resonator modes in a fully chaotic open-sided two-dimensional laser resonator is theoretically investigated in the short wavelength limit. We derive a periodic-orbit-sum formula for eigenvalues of the resonator modes by applying the semiclassical approximation to the extended Fox-Li mode calculation method. With this formula, we show that the complicated wavelength dependence of the power-coupling coefficients of the fully chaotic quasi-stadium laser resonator can be explained by a few kinds of unstable periodic orbits.

- Authors:

- Department of Communication Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197 (Japan)
- (Japan)
- Department of Nonlinear Science, ATR Wave Engineering Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288 (Japan)
- Institute for Theoretical Physics, University of Bremen, D-28359 Bremen (Germany)

- Publication Date:

- OSTI Identifier:
- 20974641

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.023816; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COUPLING; EIGENVALUES; FREQUENCY DEPENDENCE; LASER CAVITIES; LASERS; OPTICAL MODES; ORBITS; PERIODICITY; RESONATORS; SEMICLASSICAL APPROXIMATION; TWO-DIMENSIONAL CALCULATIONS; WAVELENGTHS

### Citation Formats

```
Fukushima, Takehiro, Department of Nonlinear Science, ATR Wave Engineering Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Harayama, Takahisa, and Wiersig, Jan.
```*Ray-wave correspondence in an unstable quasistadium laser resonator*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.023816.

```
Fukushima, Takehiro, Department of Nonlinear Science, ATR Wave Engineering Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Harayama, Takahisa, & Wiersig, Jan.
```*Ray-wave correspondence in an unstable quasistadium laser resonator*. United States. doi:10.1103/PHYSREVA.73.023816.

```
Fukushima, Takehiro, Department of Nonlinear Science, ATR Wave Engineering Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Harayama, Takahisa, and Wiersig, Jan. Wed .
"Ray-wave correspondence in an unstable quasistadium laser resonator". United States.
doi:10.1103/PHYSREVA.73.023816.
```

```
@article{osti_20974641,
```

title = {Ray-wave correspondence in an unstable quasistadium laser resonator},

author = {Fukushima, Takehiro and Department of Nonlinear Science, ATR Wave Engineering Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288 and Harayama, Takahisa and Wiersig, Jan},

abstractNote = {The relation between unstable periodic orbits and resonator modes in a fully chaotic open-sided two-dimensional laser resonator is theoretically investigated in the short wavelength limit. We derive a periodic-orbit-sum formula for eigenvalues of the resonator modes by applying the semiclassical approximation to the extended Fox-Li mode calculation method. With this formula, we show that the complicated wavelength dependence of the power-coupling coefficients of the fully chaotic quasi-stadium laser resonator can be explained by a few kinds of unstable periodic orbits.},

doi = {10.1103/PHYSREVA.73.023816},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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